Answer:
y - 5 = 3(x - 1)
Explanation:
Step 1: Find the equation of the line in slope-intercept form:
First, we can find the equation of the line in slope-intercept form, whose general equation is given by:
y = mx + b, where
- m is the slope,
- and b is the y-intercept.
1.1 Find slope, m
We can find the slope using the slope formula which is
m = (y2 - y1) / (x2 - x1), where
- (x1, y1) are one point on the line,
- and (x2, y2) are another point.
- We see that the line passes through (0, 2) and (1, 5).
- We can allow (0, 2) to be our (x1, y1) point and (1, 5) to be our (x2, y2) point:
m = (5 - 2) / (1 - 0)
m = (3) / (1)
m = 3
Thus, the slope of the line is 3.
1.2 Find y-intercept, b:
The line intersects the y-axis at the point (0, 2). Thus, the y-intercept is 2.
Therefore, the equation of the line in slope-intercept form is y = 3x + 2
Step 2: Convert from slope-intercept form to point-slope form:
All of the answer choices are in the point-slope form of a line, whose general equation is given by:
y - y1 = m(x - x1), where
- (x1, y1) are any point on the line,
- and m is the slope.
We can again allow (1, 5) to be our (x1, y1) point and we can plug in 3 for m:
y - 5 = 3(x - 1)
Thus, the answer is y - 5 = 3(x - 1)